Complex Ginzburg–Landau equation with generalized finite differences
In this paper we obtain a novel implementation for irregular clouds of nodes of the meshless method called Generalized Finite Difference Method for solving the complex Ginzburg–Landau equation. We derive the explicit formulae for the spatial derivative and an explicit scheme by splitting the equatio...
| Autores: | , , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/7727 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/7727 |
| Access Level: | acceso abierto |
| Palabra clave: | 517 Ginzburg–Landau equation parabolic-parabolic systems generalized finite difference method Ecuación de Ginzburg-Landau Matemáticas (Matemáticas) Análisis matemático 12 Matemáticas 1202 Análisis y Análisis Funcional |
| Sumario: | In this paper we obtain a novel implementation for irregular clouds of nodes of the meshless method called Generalized Finite Difference Method for solving the complex Ginzburg–Landau equation. We derive the explicit formulae for the spatial derivative and an explicit scheme by splitting the equation into a system of two parabolic PDEs. We prove the conditional convergence of the numerical scheme towards the continuous solution under certain assumptions. We obtain a second order approximation as it is clear from the numerical results. Finally, we provide several examples of its application over irregular domains in order to test the accuracy of the explicit scheme, as well as comparison with other numerical methods. |
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